The expression given is \( 16a - 49 \). This polynomial is in the form of a difference of squares.

The general form for factoring a difference of squares is:

\[
x^2 - y^2 = (x + y)(x - y)
\]

First, recognize that \( 16a \) and \( 49 \) are both perfect squares:

- \( 16a \) can be written as \( (4\sqrt{a})^2 \).
- \( 49 \) can be written as \( 7^2 \).

So, the expression \( 16a - 49 \) can be rewritten as:

\[
(4\sqrt{a})^2 - 7^2
\]

Now, apply the difference of squares formula:

\[
16a - 49 = (4\sqrt{a} + 7)(4\sqrt{a} - 7)
\]

So, the factored form of the polynomial is \( \boxed{(4\sqrt{a} + 7)(4\sqrt{a} - 7)} \).

Would you like more details or have any questions?

Here are some related questions:

1. How do you recognize a difference of squares in polynomials?
2. What is the difference of squares method used for?
3. Can you factor higher degree polynomials using the difference of squares?
4. How do you handle a polynomial that isn’t a perfect square?
5. What are some examples of polynomials that cannot be factored?
6. How do you verify your factorization of a polynomial?
7. What are some other methods for factoring polynomials?
8. How do you factor trinomials?

**Tip:** When factoring, always check if the polynomial can be expressed as a difference of squares—it can simplify the process significantly.

Learn how to factor the polynomial 16a - 49 using the difference of squares method. Understand the steps involved in recognizing and applying this factorization technique. Suitable for high school students studying algebra.

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